Hee-chan Lew Korea National University of Education hclew@knue.ac.kr Some Characteristics in Korean National Curriculum and its Revising Process Hee-chan Lew Korea National University of Education hclew@knue.ac.kr

Topics 7th National Curriculum Revising Process Nature, Structure, Contents, Guide line for instruction and evaluation, College Entrance Examination (CSAT) Revising Process Revision Period, Revising Team, Influencing factors in determining mathematics curriculum Social Background of Korea Some lessons from TIMSS report

Social Background Parents’ Concern on Education Education: The most important factor to understand Korean Society. Korean parents are willing to submit themselves to their children’s education. KEDI(2004): in 2000 Government’s expense for public education is 30 billion US$ Parents’ expense for out-of-school programs: 37 billion US$ (10% of their total income)

Out-of-School Programs Status of out-of-school program in society 84.1% of students (Elementary 91.1%, Junior High 81.5, Senior High 70.2%) go to extracurricular programs “Their children must study harder than other students to enter better universities” “A better university is a shortcut to a better future” Competition-Oriented Society Old tradition

Examination Tradition In 958 AD, “Koryeo ” Kingdom (918-1392) accepted from China the formal examination system to select government officials, which was kept even during the next “Chosun ” Kingdom (1392-1910) for 950 years. Pass to the examination was the most honorable event of the person and his family

“Education was our only hope ” The Poster of the Special Exhibition of Educational Materials for the 60th Anniversary of the restoration of independence: 1945-2005 “Education was our only hope” is a pregnant one-sentence to represent the 60 years of Korean Society

What is learned in out-of-school program? Techniques vs. Abilities 70-90 % of students study mathematics 1-2 hours almost every day at their out-of-school programs They learn technical skills and knowledge for eventually preparing for the college entrance examination rather than cultivating mathematical abilities They learn techniques to select correct answers in various objective tests.

International Test We worry that this kind of out-of-school studies seems to be one of the main reasons of Korean students’ high achievement in TIMSS, TIMSS-R and PISA Other presumed reasons: Korean teachers teach systematically Korean math curriculum favors TIMSS Korea Scholastic Ability Test is similar to PISA Students study hard in their schools to enter better universities or for other purposes etc.

Math Education after TIMSS There were many changes after TIMSS 7th National Curriculum issued on December 1997 Focusing on students’ problem solving abilities School Reform Movement in the late of 1990s Open Education Performance Assessment Computer use in classroom

Three factors for change Gradual change in mathematics education since 1980 to support the economic development of 1970s and 1980s From “theoretical” mathematics to “practical” mathematics TIMSS report Reflection on the weak points of math classes Impact of foreign curricula such as of USA & Great Britain

TIMSS report TIMSS provided an opportunity for Korean Society to reflect on the educational environment on the whole through a multivariate analysis with teachers, institutions as well as students. Korean mathematics education seems to have many serious weak points, despite of students' very proud achievement.

Affective Characteristics: Lesson from TIMSS Report Korean students' affective characteristics was not friendly to mathematics compared with other countries. In the case of the 8th grade, Korea was one of the lowest countries in the confidence and interest levels. This result is also being repeated in the current PISA test.

Achievement Difference: Lesson from TIMSS Report There is a significant difference in the achievement level between male and female, and city and rural area A serious problem with respect to an equal opportunity in mathematics education. Traditional custom guides girls not to go to the mathematical fields. Generally rural area, compared with city area, has an educationally inferior environment.

Teaching Style: Lesson from TIMSS Report Whole class activities under teachers' control is the first consideration in the style of organizing classes 89% of students, the largest rate, thought that whole class lesson with teacher’s explanation is the most frequent style. Only 11%, the lowest rate, of students thought that activities worked in pairs or small groups with assistance from teachers is the most frequent style.

Technology: Lesson from TIMSS Report Korean math teachers were the most negative in using computer and calculator in their classes and problem solving process 93% of teachers and 96% of students never used computers and calculators in their math classes, which was the highest among TIMSS countries

Goals for learning mathematics: Lesson from TIMSS Report Many math teachers do not consider mathematical application and reasoning ability as important goals for students. Korea belongs to countries whose rate was very low. Teachers seem not to understand well the reason why problem solving should be emphasized in mathematics education

Evaluation Method: Lesson from TIMSS Report Critics have been proposed that the objective items might give a better chance for Korean students to get higher scores than other nations’ students because Korean students were familiar with an objective test.

The 7th curriculum Issued in Dec 31 1997 to reflect: Reform movement of mathematics education throughout the world, particularly of USA Reconsideration of learning methods and contents school mathematics has emphasized for a long time Lessons from TIMSS report National goals for the construction of an advanced civilized society Individual differences in abilities, needs, and interests of students

Nature: practical mathematics The new curriculum emphasizes practical mathematics such as problem solving application and modeling of mathematics reasoning It contrasts sharply with the 3rd curriculum issued in 1973 which emphasized mathematical knowledge as theoretical aspect

Gradual change since 1980 The change has been done gradually since the 4th curriculum issued in 1980: 4th: problem solving 5th: problem solving 6th: problem solving, technology 7th: problem solving, reasoning, communication, technology, connection, modeling The influence of USA for Korean mathematics curriculum

Old Kingdom Period Korea has a long history of emphasizing theoretical mathematics for a selective examination In 958, the "Koryeo" Kingdom (918-1392) introduced mathematics into its examination system to select middle level technical government officials. They have to memorize many Chinese mathematical classics including “Nine Chapters on Mathematical Art” for 7-9 years in schools.

1st Curriculum 1st curriculum issued in 1955 professed to emphasize practical problem solving in real life under the influence of the American pragmatism and Dewey's educational philosophy. However, real situation was different because most of textbook authors were pure mathematicians and the college entrance examination were not practically oriented .

2nd & 3rd Curriculum 2nd curriculum (1963) emphasized more formal and systematical mathematics. 3rd curriculum (1973) accepted the new mathematics movement totally, emphasizing set language, mathematical structures and logical rigorousness The theoretical mathematics reached to the highest points.

History of Korean Curriculum

Instruction under 7th curriculum The 7th curriculum emphasizes various types of instruction to improve efficiency and significance of students' mathematical learning. It recommends that students should be able to experience the joy of discovery and maintain their interest in mathematics in their classrooms

Evaluation under 7th curriculum Mathematical power should be evaluated by the following methods in their classrooms: to focus on students' understanding of a problem and the problem-solving process as well as its results; to focus on student's abilities to think and solve problems in a flexible, diverse and creative fashion;

Schooling system & Students number Korea has 6-3-3-4 educational system Elementary 6 years, Junior High 3 years, Senior High 3 years, College 4 years We have about 400,000 students in each grade Almost 100 % students graduate Senior High schools At 11 grade, they choose one of the Liberal Arts track or Science track The ratio of students of Liberal Arts track and Science track is 2:1

Structure The 7th curriculum have two parts: The compulsory core curriculum learned in the first 10 school years called “people common educational period” The elective curriculum learned in 11 and 12 grades by choosing some among 6 subjects such as: Real-World Math, Math I, Math II, Calculus, Statistics and Probability, and Discrete Math

Structure The compulsory core curriculum is to teach same contents to all students The elective curriculum has two kinds of selective subject: General-selective: a subject to strengthen cultural literacy and connection to real world Real-World Mathematics Deep-selective: 5 subjects related with college entrance examination Math I, Math II, Calculus, Statistics and Probability, and Discrete Math

Structure of the 7th Curriculum School Elementary Junior High Senior High Grade 1 2 3 4 5 6 7 8 9 10 11 12 Level 1a 1b 2a 2b 3a 3b 4a 4b 5a 5b 6a 6b 7a 7b 8a 8b 9a 9b 10a 10b Curri Name Compulsory Core Curriculum Selective Subject Mathematics (general-selective) Real World Math (deep selective) Math I, Math II, Calculus, Probability & Statistic, Discrete Mathematics

Level Promotion The compulsory core curriculum has 20 levels. Students are promoted by a level-transfer test administered by schools at the end of semester. This system converts from the laissez-fair policy which guarantees automatic promotion to the controlling policy. Students who fail the level transfer test by scoring below 60% must take the extra- course offered by schools during the vacation of the semester.

Enrichment and Supplement Program To avoid unnecessary competition and a sense of incongruity among students and parents, skipping levels is not permitted For advanced students and low achievers, special enrichment and supplementary sections will be provided during the course at the teacher's discretion.

Time Allotment Time allotted to Mathematics of 1-10 grades is 131 class hours in average per year. It is the largest amount of time allotment second only to Korean, of which time allotment is 188 hours in average per year. In Grades 11 & 12, the time allotment depends on the kinds of students’ track for College Entrance Examination:“Science” and “Liberal art”

Time Allotment School Elementary Junior High Senior High Grade 1 2 3 4 5 6 7 8 9 10 11 12 Curri Name Compulsory Core Curriculum Selective Class hours* Per year** 120 136 102 Liberal Arts Science 272 Science272 Class hours per week 3-4 Science 4 *1 class hour of Elementary, Junior High and Senior High is 40, 45, 50 minutes respectively ** 1 year is 34 weeks

Contents of Grades 1-10 The Compulsory mathematics curriculum consists of the six strands: Number & Operation, Geometry, Measuring, Probability & Statistics, Letter & Expression, and Pattern & Function Unlike USA, Korea does not distinguish content strand and process strand. Only exception is “problem solving” but, it is in “Letters and Expression” strand.

Class Hours classified by Strands Ratio Number and Operation 448 34.2% Geometry 290 22.1% Measuring 158 12.1% Probability and Statistics 98 7.5% Letter and Expression 197 15.0% Pattern and Function 119 9.1% Total 1310 100%

Class Hours classified by Strands and Grades 1 2 3 4 5 6 7 8 9 10 Number & Operation 74 62 63 46 80 58 59 44 32 24 34 25 13 21 15 Geometry 11 22 16 18 35 26 19 48 30 29 Measuring 14 17 12 20 23 Probability & Statistics Letter & Expression 39 28 27 43 31 Pattern & Function 33 Sum 120 100 136 102

Number and Operation Class hours classified by big ideas and grades Elementary Junior High S. H. Total 1 2 3 4 5 6 7 8 9 10 Natural Number 74 62 63 46 70 51 27 20 17 13 18 269 20.5 Fraction & Decimal Fraction 36 26 42 31 32 24 120 9.2 Integer & Rational Number 16 12 25 1.9 Real & Complex Number 21 15 34 2.6 Sum 80 58 59 44 448 34.2 Class Hours per year: 1310 (1st grade, 102; 9th grade, 120; others, 136)

Geometry Class hours classified by big ideas and grades Elementary Junior High S. H. Total 1 2 3 4 5 6 7 8 9 10 Spatial Sense 13 11 16 12 67 5.1 Properties of Figures 14 33 24 28 19 18 21 15 144 11.0 Deductive Proof 17 30 29 54 4.1 Coordinate Geometry 25 1.9 Sum 22 35 26 32 23 34 48 290 22.1 Class Hours per year: 1310 (1st grade, 102; 9th grade, 120; others, 136)

Measuring Class hours classified by big ideas and grades Elementary Junior High S. H. Total 1 2 3 4 5 6 7 8 9 10 Measuring with Units 22 16 13 20 14 17 18 106 8.1 Quantity Sense and Estimation 33 2.5 Trigonometric Ratio 11 0.8 Linear Programming 0.6 Sum 24 15 12 23 158 12.1 Class Hours per year: 1310 (1st grade, 102; 9th grade, 120; others, 136)

Probability and Statistics Class hours classified by big ideas and grades Class Hours per year: 1310 (1st grade, 102; 9th grade, 120; others, 136) Big Ideas Elementary Junior High S. H. Total 1 2 3 4 5 6 7 8 9 10 Diagram and Graphs 45 3.4 Probability 14 24 1.8 Basic Statistics 13 29 2.2 Sum 18 98 7.5

Letter and Expression Class hours classified by big ideas and grades Elementary Junior High S. H. Total 1 2 3 4 5 6 7 8 9 10 Making Expression 14 17 13 50 3.8 Equation & Inequality 12 25 18 21 15 78 6.0 Factorization 0.9 Problem Solving Strategy 57 4.4 Sum 22 16 39 28 27 43 31 197 15.0 Class Hours per year: 1310 (1st grade, 102; 9th grade, 120; others, 136)

Pattern and Function Class hours classified by big ideas and grades Elementary Junior High S. H. Total 1 2 3 4 5 6 7 8 9 10 Pattern Finding 16 1.2 Ratio & Proportion 23 17 29 2.2 Elementary Function 18 13 14 15 11 56 4.3 Trigonometric Function 1.4 Sum 33 24 119 9.1 Class Hours per year: 1310 (1st grade, 102; 9th grade, 120; others, 136)

College Entrance Examination and Mathematics Curriculum Area Examination Scope Number of items Total Time Type of problems Type A (130,000) (100,000) MathⅠ 40% MathⅡ 40% Select 1 among Calculus, Statistics and probability, Discrete math 20% 30 items 100 Minutes Choice:70%, Short Answer:30% Type B (270,000) (300,000) Math I

Revising Period of Curriculum 2nd - 4th curriculum : 7-10 years 5th - 7th curriculum: 5 years Curriculum 1st 2nd 3rd 4th Revising Date 1955. 8. 1 E, H 1963. 2. 15 E, J, S 1973. 2. 14 E 1973. 8. 31 J 1974 S 1981. 12. 31 5th 6th 7th The newly developed 1987. 3. 31 J 1987. 6. 30 E 1988. 3. 31 S 1992. 6. 30 J 1992. 9. 30 E 1992. 10. 30 S 1997. 12. 30 2005. 12. 30 Grade 1-10 2006. 12. 30 Grade 11-12

Revising Team MOE names one person in a university or a research institute as the chief of the revising team and requests the chief to construct the revising team 7th: one professor of SKK University The newly developed: The director of Korea Institute of Curriculum and Evaluation (KICE) The chief has an important role in the selection process of other 6-7 members who are all professors or researchers

Activities of the Revising Team The team holds a conference to reflect various opinions from various individual or groups like academic circles or society and math teacher’s union or groups The team makes questionnaire and interview with teachers, researchers, parents, students, administrators to appreciate national or societal goals and to select contents and their sequence.

Consulting Team The team has the consulting team with teachers and professors to consult various problems in the process of revising the curriculum. Several meetings are held to respond to questions and some issues raised by the revising team

Meetings to reflect various opinions The mathematics education society invites the chief of the team to introduce the draft of the curriculum at the annual meeting of the Society to provide some feedback to the team. The team holds seminars on the draft of the curriculum 5-6 times at the focal universities in the local areas to reflect some ideas of the local communities of mathematics education.

Reviewing Committee MOE organizes the reviewing committee with professors and teachers to review the final draft corrected by the revising team based on the various opinions collected from various meetings. Reviewing Committee invites the revising team in the reviewing process to discuss or to debate some key issues.

Public Hearing After finishing the whole reviewing process, the revising team holds a public hearing to report the final draft to the public.

Important Factors in Revising Curriculum Analysis of the previous curriculum executed in classrooms. Students’ understanding level Logical sequence of contents Foreign countries’ curriculum National and social needs Request of academic circle Relevance of amount of learning

Conclusion This has summarized the change of mathematics education and the process for the change made in Korea after TIMSS. The main focus is on the practical mathematics. The national strategy to construct a highly developed country in the near future. Practical Mathematics is tool for propelling the development of science and for solving quantitative and qualitative problems faced on people in their lives.

Conclusion More students have to leave school absorbing mathematics and having confidence. Until now, school mathematics is considered as only a subject for college entrance examination. Many students think continual learning of mathematics is meaningless and elementary mathematics is enough. We have to stop this consideration from now.

Conclusion Korea has a long history of examination oriented mathematics education. So, it is very difficult to change this kind of culture. But, many Korean mathematics teachers and educators are trying to re-model math classes though it is a rugged and very difficult way.